In distributed power generation systems (DPGS), generally, one or more distributed power sources coupled with switching power converters (SPC) may provide direct or alternating current (DC or AC) to the distributed power generation network or circuit.
FIG. 1 shows an electrical network (power grid) of an exemplary AC distributed power generation system. The network 100 includes multiple individual PV strings 102A, 102B, . . . 102Z connected in parallel, each including a number of solar modules. A respective voltage source inverter 104A, 104B, 104Z is coupled with each of the PV strings 102A, 102B, . . . 102Z. The PV strings and associated voltage source inverters form multiple power sources connected with each other through cables 106, transformer 108, and cables 108 for connection to AC grid lines 112.
The distributed power generation system in FIG. 1 can be modeled by a Thevenin's equivalent circuit and a Norton's equivalent circuit (as shown in FIG. 2A). As shown in FIG. 2A, the Thevenin's equivalent circuit for the electrical network consists of an ideal voltage source Vg and a series-connected equivalent grid impedance Zg, and the Norton's equivalent circuit representing the SPC consists of the parallel-connected ideal current source Is,i and the corresponding output impedance Zo,i.
An ideal voltage source can maintain a prescribed voltage across its terminals irrespective of the magnitude of the current flowing through it. However, in the circuit in FIG. 2A, due to the existence of the grid impedance Zg and the SPC output impedance Zo,i, it is possible for the power sources to couple with each other, with their controllers interact or excite system resonances around transfer function complex conjugate poles. This may result in system instability.
FIG. 2B shows a simplified impedance modeling circuit of FIG. 2A. FIG. 3 are graphs showing magnitude and phase relationship between equivalent output impedance Zo of the switching power converters in the power sources and the equivalent grid impedance ZG in the power systems. Referring to FIGS. 2B and 3, system instability occurs when the following two conditions are satisfied:                the value of equivalent grid impedance ZG intersects with that of the equivalent SPC output impedance Zo; and        the phase difference of ZG and ZO at the intersection frequency is around 180°.        